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math.GT2011
Diagram genus, generators and applications
A. Stoimenow
We continue the study of the genus of knot diagrams, deriving a new description of generators using Hirasawa's algorithm. This description leads to good estimates on the maximal nu…
math.GT1999
Vassiliev invariants and rational knots of unknotting number one
A. Stoimenow
Introducing a way to modify knots using -trivial rational tangles, we show that knots with given values of Vassiliev invariants of bounded degree can have arbitrary unknotting n…